System and Method for Calibrating Video and Lidar Subsystems

ABSTRACT

A system uses range and Doppler velocity measurements from a lidar system and images from a video system to estimate a six degree-of-freedom trajectory of a target. The system calibrates the lidar subsystem with the video subsystem in two stages. In a first stage, the system calibrates the lidar subsystem so that lidar measurements provide 3D lidar coordinates. In a second stage, the system relates the 3D lidar coordinates with a video image obtained from the video subsystem.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/682,463, which was filed on Aug. 13, 2012, and is incorporatedherein by reference as if reproduced below in its entirety.

FIELD OF THE INVENTION

The invention is generally related to calibrating video and lidarsubsystems and more particularly, to calibrating the video and lidarsubsystems to obtain accurate three-dimensional (3D) images of a target.

BACKGROUND OF THE INVENTION

Obtaining accurate three-dimensional (3D) images of a target using atwo-dimensional (2D) video camera subsystem integrated with athree-dimensional lidar (laser radar) subsystem is difficult unless thetwo subsystems are calibrated with one another. Calibration may refer tothe registration of the two subsystems such that points on a surface ofa target are accurately mapped to one another by each of the twosubsystems (or substantially so within the measurement tolerances, etc.,of each subsystem). In other words, accurate three-dimensional imagesrequire correspondence between measurements of the 3D coordinatesobtained from the lidar subsystem with the respective pixel positions inthe 2D video image.

What is needed is an improved system and method for calibrating thevideo subsystem with the lidar subsystem of a three-dimensionalmeasurement system.

SUMMARY OF THE INVENTION

Various implementations of the invention combine measurements generatedby a a lidar system with images generated by a video system to resolve asix degrees of freedom trajectory that describes motion of a target.Once this trajectory is resolved, an accurate three-dimensional image ofthe target may be generated. In some implementations of the invention,the calibration of the lidar subsystem with the video subsystem may becarried out in two stages. In a first stage, the system calibrates thelidar subsystem so that lidar measurements provide 3D lidar coordinates.In a second stage, the system relates the 3D lidar coordinates with avideo image obtained from the video subsystem

These implementations, their features and other aspects of the inventionare described in further detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a combined lidar and video camera system according tovarious implementations of the invention.

FIG. 2 illustrates a lidar (i.e., laser radar) according to variousimplementations of the invention.

FIG. 3 illustrates a scan pattern for a lidar subsystem that employs twolidar beams according to various implementations of the invention.

FIG. 4 illustrates a scan pattern for a lidar subsystem that employsfour lidar beams according to various implementations of the invention.

FIG. 5 illustrates a relationship between points acquired from the lidarsubsystem from separate beams at substantially the same instance of timethat may be used to estimate an x-component of angular velocity of atarget according to various implementations of the invention.

FIG. 6 illustrates a relationship between points acquired from the lidarsubsystem from separate beams at substantially the same instance of timethat may be used to estimate a y-component of angular velocity of atarget according to various implementations of the invention.

FIG. 7 illustrates a relationship between points acquired from the videosubsystem that may be used to estimate a two-dimensional (e.g. x and ycomponents) translational velocity and a z-component of angular velocityof a target according to various implementations of the invention.

FIG. 8 illustrates a scan pattern of a lidar beam according to variousimplementations of the invention.

FIG. 9 illustrates a timing diagram which may be useful for describingvarious timing aspects associated with measurements from the lidarsubsystem according to various implementations of the invention.

FIG. 10 illustrates a timing diagram which may be useful for describingvarious timing aspects associated with measurements from the lidarsubsystem in relation to measurements from the video subsystem accordingto various implementations of the invention.

FIG. 11 illustrates a block diagram useful for processing lidarmeasurements and video images according to various implementations ofthe invention.

FIG. 12 illustrates a block diagram useful for processing lidarmeasurements and video images according to various implementations ofthe invention.

FIG. 13 illustrates a block diagram useful for processing lidarmeasurements and video images according to various implementations ofthe invention.

FIG. 14 illustrates a block diagram useful for processing lidarmeasurements and video images according to various implementations ofthe invention.

FIG. 15 illustrates a block diagram useful for processing lidarmeasurements and video images according to various implementations ofthe invention

FIG. 16 illustrates an example reference grid used for calibrating alidar subsystem with a video subsystem according to variousimplementations of the invention.

FIG. 17 illustrates a flowchart depicting example operations performedby a system for calibrating a lidar subsystem and a video subsystem,according to various aspects of the invention.

DETAILED DESCRIPTION

FIG. 1 illustrates a combined lidar and video camera system 100 (orthree-dimensional measurement system 100) according to variousimplementations of the invention. Various implementations of theinvention utilize synergies between lidar measurements and video imagesto resolve six degrees of freedom for motion of a target to a degree nototherwise possible with either a lidar or video camera alone.

Combined system 100 includes a lidar subsystem 130, a video subsystem150, and a processing system 160. As illustrated, lidar subsystem 130includes two or more lidar beam outputs 112 (illustrated as a beam 112A,a beam 112B, a beam 112(n−1), and a beam 112 n); two or more reflectedbeam inputs 114 each corresponding to one of beams 112 (illustrated as areflected beam 114A, a reflected beam 1146, a reflected beam 114(n−1),and a reflected beam 114 n); two or more lidar outputs 116 eachassociated with a pair of beam 112/reflected beam 114 (illustrated as alidar output 116A associated with beam 112A/reflected beam 114A, a lidaroutput 116B associated with beam 112B/reflected beam 114B, a lidaroutput 116(n−1) associated with beam 112(n−1)/reflected beam 114(n−1),and a lidar output 116 n associated with beam 112 n/reflected beam 114n).

In some implementations of the invention, beam steering mechanism 140may be employed to steer one or more beams 112 toward target 190. Insome implementations of the invention, beam steering mechanism 140 mayinclude individual steering mechanisms, such as a steering mechanism140A, a steering mechanism 140B, a steering mechanism 140C, and asteering mechanism 140D, each of which independently steers a beam 112toward target 190. In some implementations of the invention, one beamsteering mechanism 140 may independently steer pairs or groups of beams112 toward target 190.

In some implementations of the invention, beam steering mechanism 140may include one or more mirrors, each of which may or may not beseparately controlled, each mirror steering one or more beams 112 towardtarget 190. In some implementations of the invention, beam steeringmechanism 140 may directly steer an optical fiber of beam 112 withoutuse of a mirror. In some implementations of the invention, beam steeringmechanism 140 may be controlled to steer beams 112 in azimuth and/orelevation. Various techniques may be used by beam steering mechanism 140to steer beam(s) 112 toward target 190 as would be appreciated.

In some implementations of the invention, beam steering mechanism 140may be used to control both an azimuth angle and an elevation angle oftwo beams 112 toward the target. By controlling both the azimuth angleand the elevation angle, the two beams 112 may be used to scan a volumefor potential targets or track particular targets such as target 190.Other scanning mechanisms may be employed as would be apparent. In someimplementations of the invention, the two beams 112 may be offset fromone another. In some implementations of the invention, the two beams 112may be offset vertically (e.g., in elevation) or horizontally (e.g., inazimuth) from one another by a predetermined offset and/or apredetermined angle, either of which may be adjustable or controlled.

In some implementations of the invention, beam steering mechanism 140may be used to control both an azimuth angle and an elevation angle offour beams 112 toward the target. In some implementations, the fourbeams 112 may be arranged with horizontal and vertical separations. Insome implementations, the four beams may be arranged so as to form atleast two orthogonal separations. In some implementations, the fourbeams may be arranged in a rectangular pattern, with pairs of beams 112offset from one another vertically and horizontally. In someimplementations, the four beams may be arranged in other patterns, withpairs of beams 112 offset from one another. The separations of the fourbeams 112 may be predetermined offsets and/or predetermined angles,which may be fixed, adjustable and/or controlled.

A certain portion of each beam 112 may be reflected back from target 190to lidar subsystem 130 as reflected beam 114. In some implementations ofthe invention and as illustrated in FIG. 1, reflected beam 114 followsthe same optical path (though in reverse) as beam 112. In someimplementations of the invention, a separate optical path may beprovided in lidar subsystem 130 or in combined system 100 to accommodatereflected beam 114.

In some implementations of the invention, lidar subsystem 130 receives areflected beam 114 corresponding to each beam 112, processes reflectedbeam 114, and outputs lidar output 116 to processing system 160.

Combined system 100 also includes video subsystem 150. Video subsystem150 may include a video camera for capturing two dimensional images 155of target 190. Various video cameras may be used as would be apparent.In some implementations of the invention, the video camera may outputimages 155 as pixels at a particular resolution and at a particularimage or frame rate. Video images 155 captured by video subsystem 150are forwarded to processing system 160. In some implementations of theinvention, lidar subsystem 130 and video subsystem 150 are offset fromone another in terms of position and orientation. In particular, lidarmeasurements typically correspond to three dimensions (e.g., x, y, andz) whereas video images typically correspond to two dimensions (e.g., xand y). Various implementations of invention calibrate lidar subsystem130 with video subsystem 150 to ensure that data provided by each systemrefers to the same location in a given coordinate system as would beapparent.

Combined system 110 may include one or more optional video subsystems(not otherwise illustrated) for capturing additional two-dimensionalimages 155 of target 190 from different positions, perspectives orangles as would be apparent.

In some implementations of the invention, processing system 160 receiveslidar outputs 116 from lidar subsystem 130 and images 155 from videosubsystem 150 and stores them in a memory or other storage device 165for subsequent processing. Processing system 160 processes lidar outputs116 and images 155 to generate a three-dimensional image of target 190.In some implementations of the invention, processing system 160determines a trajectory of target 190 from a combination of lidaroutputs 116 and images 155 and uses the trajectory to generate a motionstabilized three-dimensional image of target 190.

In some implementations of the invention, lidar subsystem 130 mayinclude, for each of beams 112, a dual frequency, chirped coherent laserradar system capable of unambiguously and simultaneously measuring bothrange and Doppler velocity of a point on target 190. Such a laser radarsystem is described in co-pending U.S. application Ser. No. 11/353,123,entitled “Chirped Coherent Laser Radar System and Method,” (the “ChirpedLidar Specification”), which is incorporated herein by reference in itsentirety. For purposes of clarity, a “beam” referenced in the ChirpedLidar Specification is not the same as a “beam” referred to in thisdescription. More particularly, in the Chirped Lidar Specification, twobeams are described as output from the laser radar system, namely afirst beam having a first frequency (chirped or otherwise) and a secondbeam having a second frequency (chirped or otherwise) that aresimultaneously coincident on a point on a target to provide simultaneousmeasurements of both range and Doppler velocity of the point on thetarget. For purposes of simplicity and clarity, a singular “beam” asdiscussed herein may refer to the combined first and second beams outputfrom the laser radar system described in the Chirped LidarSpecification. The individual beams discussed in the Chirped LidarSpecification are referred to herein henceforth as “signals.”Nonetheless, various implementations of the invention may employ beamsother than those described in the Chirped Lidar Specification providedthese beams provide simultaneous range and Doppler velocity measurementsat points on the target.

FIG. 2 illustrates a lidar 210 that may be used to generate and processbeam 112 and reflected beam 114 to provide lidar output 116 according tovarious implementations of the invention. Each lidar 210 unambiguouslydetermines a range and Doppler velocity of a point on target 190relative to lidar 210. Lidar 210 includes a first frequency lidarsubsection 274 and a second frequency lidar subsection 276. Firstfrequency lidar subsection 274 emits a first frequency target signal 212toward target 190 and second frequency lidar subsection 276 emits asecond frequency target signal 214 toward target 190. The frequencies offirst target signal 212 and second target signal 214 may be chirped tocreate a dual chirp system.

First frequency lidar subsection 274 may include a laser sourcecontroller 236, a first laser source 218, a first optical coupler 222, afirst signal delay 244, a first local oscillator optical coupler 230,and/or other components. Second frequency lidar subsection 276 mayinclude a laser source controller 238, a second laser source 220, asecond optical coupler 224, a second signal delay 250, a second localoscillator optical coupler 232 and/or other components.

First frequency lidar subsection 274 generates first target signal 212and a first reference signal 242. First target signal 212 and firstreference signal 242 may be generated by first laser source 218 at afirst frequency that may be modulated at a first chirp rate. Firsttarget signal 212 may be directed toward a measurement point on target190 either independently or combined with second target signal 214.First frequency lidar subsection 274 may combine target signal 256 thatwas reflected from target 190 with first reference signal 242, which isdirected over a path with a known or otherwise fixed path length, toresult in a combined first target signal 262.

Second frequency lidar subsection 276 may be collocated and fixed withrespect to first frequency lidar subsection 274 (i.e., within lidar210). More particularly, the relevant optical components fortransmitting and receiving the respective laser signals may becollocated and fixed. Second frequency lidar subsection 276 may generatesecond target signal 214 and a second reference signal 248. Secondtarget signal 214 and second reference signal 248 may be generated bysecond laser source 220 at a second frequency that may be modulated at asecond chirp rate. In some implementations of the invention, the secondchirp rate is different from the first chirp rate.

Second target signal 214 may be directed toward the same measurementpoint on target 190 as first target beam 212. Second frequency lidarsubsection 276 may combine one portion of target signal 256 that wasreflected from target 190 with second reference signal 248, which isdirected over a path with a known or otherwise fixed path length, toresult in a combined second target signal 264.

Processor 234 receives combined first target signal 262 and combinedsecond target signal 264 and measures a beat frequency caused by adifference in path length between each of the reflected target signalsand its corresponding reference signal, and by any Doppler frequencycreated by target motion relative to lidar 210. The beat frequencies maythen be combined linearly to generate unambiguous determinations ofrange and Doppler velocity of target 190 as set forth in the ChirpedLidar Specification. In some implementations, processor 234 provides therange and Doppler velocity measurements to processing system 160. Insome implementations, processor 234 is combined with processing system160; in such implementations, processing system 160 receives combinedfirst target signal 262 and combined second target signal 264 and usesthem to determine range and Doppler velocity.

As described, each beam 112 provides simultaneous measurements of rangeand Doppler velocity of a point on target 190 relative to lidar 210.According to various implementations of the invention, various numbersof beams 112 may be used to provide these measurements of target 190. Insome implementations of the invention, two or more beams 112 may beused. In some implementations of the invention, three or more beams 112may be used. In some implementations of the invention four or more beams112 may be used. In some implementations of the invention, five or morebeams 112 may be used.

In various implementations of the invention, beams 112 may be used togather measurements for different purposes. For example, in someimplementations of the invention, a particular beam 112 may be used forpurposes of scanning a volume including target 190. In someimplementations of the invention, multiple beams 112 may be used toaccomplish such scanning. In some implementations of the invention, aparticular beam 112 may be used to monitor a particular feature orposition on target 190. In some implementations of the invention,multiple beams 112 may be used to independently monitor one or morefeatures and/or positions on target 190. In some implementations of theinvention, one or more beams 112 may be used to scan target 190 whileone or more other beams 112 may be used to monitor one or more featuresand/or positions on target 190.

In some implementations of the invention, one or more beams 112 may scantarget 190 to obtain a three dimensional image of target 190 while oneor more other beams 112 may be monitoring one or more features and/orpositions on target 190. In some implementations of the invention, aftera three dimensional image of target 190 is obtained, one or more beams112 may continue scanning target 190 to monitor and/or update the motionaspects of target 190 while one or more other beams 112 may monitor oneor more features and/or positions on target 110.

In some implementations of the invention, measurements obtained via oneor more beams 112 used to monitor and/or update the motion aspects oftarget 190 may be used to compensate measurements obtained via the oneor more other beams 112 used to monitor one or more features and/orpositions on target 190. In these implementations of the invention, thegross motion of target 190 may be removed from the measurementsassociated with various features and/or positions on target 190 toobtain fine motion of particular points or regions on target 190. Invarious implementations of the invention, fine motion of target 190 mayinclude various vibrations, oscillations, or motion of certain positionson the surface of target 190 relative to, for example, a center of mass,a center of rotation, another position on the surface of target 190 orother position. In various implementations of the invention, fine motionof target 190 may include, for example, relative motion of variousfeatures such as eyes, eyelids, lips, mouth corners, facial muscles ornerves, nostrils, neck surfaces, etc. or other features of target 190.

In some implementations of the invention, based on the gross motionand/or the fine motion of target 190, one or more physiologicalfunctions and/or physical activities of target 190 may be monitored. Forexample, co-pending U.S. patent application Ser. No. 11/230,546,entitled “System and Method for Remotely Monitoring PhysiologicalFunctions” describes various systems and methods for monitoringphysiological functions and/or physical activities of an individual andis incorporated herein by reference in its entirety.

In some implementations of the invention, one or more beams 112 may beused to monitor one or more locations on an eyeball of target 190 andmeasure various position and motion aspects of the eyeball at the eachof these locations. Co-pending U.S. patent application Ser. No.11/610,867, entitled “System and Method for Tracking Eyeball Motion”describes various systems and methods for tracking the movement of aneyeball and is incorporated herein by reference in its entirety.

In some implementations of the invention, one or more beams 112 may beused to focus on various features or locations on a face of target 190and measure various aspects of the face with respect to the features orlocations on the face of target 190. For example, certain facialfeatures or facial expressions may be monitored over a period of time toinfer a mental state of target 190, to infer an intent of target 190, toinfer a deception level of target 190 or to predict an event associatedwith target 190 (e.g., certain facial muscles may twitch just prior to achange in expression or prior to speech).

In some implementations of the invention, one or more beams 112 may beused to monitor one or more locations on a neck of target 190. Themeasured motion aspects of the neck of target 190 may be used todetermine throat movement patterns, vocal cord vibrations, pulse rate,and/or respiration rate. In some implementations of the invention, oneor more beams 112 may be used to monitor one or more locations on anupper lip of target 190 to detect and measure vibrations associated withspeech of target 190. These vibrations may be used to substantiallyreproduce the speech of target 190.

In some implementations of the invention, one or more beams 112 mayserve one purpose during a first period or mode of operation of combinedsystem 100 and may switch to serve a different purpose during a secondperiod or mode of operation of combined system 100. For example, in someimplementations of the invention, multiple beams 112 may be used tomeasure various motion aspects of target 190 so that processing system160 may determine or acquire a trajectory of target 190. Once thetrajectory of target 190 is acquired, some of the multiple beams 112 mayswitch to monitoring certain other aspects or features of target 190while other ones of the multiple beams 112 measure motion aspects oftarget 190 so that its trajectory can be maintained.

In some implementations of the invention, five beams 112 scan target 190to obtain a three dimensional image of target 190. In theseimplementations, four of these beams 112 each scan a portion of target190 (using various scanning patterns as described in further detailbelow) while a fifth beam 112 performs an “overscan” of target 190. Theoverscan may be a circular, oval, elliptical or similar round scanpattern or a rectangular, square, diamond or similar scan pattern orother scan pattern useful for capturing multiple measurements of variouspoints on target 190 (or at least points within close proximity to oneanother) within relatively short time intervals. These multiplemeasurements may correspond to other measurements made by the fifth beam112 (i.e., multiple visits to the same point by the fifth beam 112) orto measurements made by one or more of the other four beams 112 (i.e.,visits to the same point by the fifth beam and one or more of the otherfour beams 112). In some implementations, the pattern of the overscanmay be selected to provide additional vertical and/or horizontal spreadbetween measurements of target 190. Both the multiple measurements andadditional spread may be used to improve estimates of the motion oftarget 190. Use of the fifth beam 112 to overscan target 190 may occurduring each of the different modes of operation referred to above.

In some implementations of the invention, once the trajectory of target190 is satisfactorily acquired, one or more beams 112 may providemeasurements useful for maintaining the trajectory of target 190 as wellas monitor other aspects of features of target 190. In suchimplementations, other beams 112 may be used to scan for other targetsin the scanning volume.

As illustrated in FIG. 1, a target coordinate frame 180 may be used toexpress various measurements associated with target 190. Variouscoordinate frames may be used as would be appreciated. In someimplementations of the invention, various ones of the subsystems 130,150 may express aspects of target 190 in coordinate frames other thantarget coordinate frame 180 as would be appreciated. For example, insome implementations of the invention, a spherical coordinate frame(e.g., azimuth, elevation, range) may be used to express measurementsobtained via lidar subsystem 130. Also for example, in someimplementations of the invention, a two dimensional pixel-basedcoordinate frame may be used to express images 155 obtained via videosubsystem 150. Various implementations of the invention may use one ormore of these coordinate frames, or other coordinate frames, at variousstages of processing as will be appreciated.

As would be appreciated, in some implementations of the invention,various coordinate transformations may be required to transformmeasurements from lidar subsystem 130, which may be expressed in aspherical coordinates with reference to lidar subsystem 130 (sometimesreferred to as a lidar measurement space), to the motion aspects oftarget 190, which may be expressed in Cartesian coordinates withreference to target 190 (sometimes referred to as target space).Likewise, various coordinate transformations may be required totransform measurements from video subsystem 150, which may be expressedin Cartesian or pixel coordinates with reference to video subsystem 150(sometimes referred to as video measurement space), to the motionaspects of target 190. In addition, measurements from combined system100 may be transformed into coordinate frames associated with externalmeasurement systems such as auxiliary video, infrared, hyperspectral,multispectral or other auxiliary imaging systems. Coordinatetransformations are generally well known.

As would be appreciated, in some implementations of the invention,various coordinate transformations may be required to transformmeasurements from lidar subsystem 130 and/or video subsystem 150 toaccount for differences in position and/or orientation of each suchsubsystem 130, 150 as would be apparent.

FIG. 3 illustrates a scan pattern 300 which may be used to scan a volumefor targets 190 according to various implementations of the invention.Scan pattern 300 includes a first scan pattern section 310 and a secondscan pattern section 320. First scan pattern section 310 may correspondto a scan pattern of a first beam 112 (e.g., beam 112A) that may be usedto scan the volume (or portion thereof). Second scan pattern section 320may correspond to a scan pattern of a second beam 112 (e.g., beam 112B)that may be used to scan the volume (or portion thereof).

As illustrated in FIG. 3, the first beam 112 scans an upper region ofscan pattern 300 whereas the second beam 112 scans a lower region ofscan pattern 300. In some implementations of the invention, the scanpattern sections 310, 320 may include an overlap region 330. Overlapregion 330 may be used to align or “stitch together” first scan patternsection 310 with second scan pattern section 320. In someimplementations of the invention, scan patterns 310, 320 do not overlapto form overlap region 330 (not otherwise illustrated).

In implementations of the invention where lidar subsystem 130 employs avertically displaced scan pattern 300 (such as that illustrated in FIG.3), first beam 112 is displaced vertically (i.e., by some verticaldistance, angle of elevation, or other vertical displacement) from asecond beam 112. In this way, the pair of beams 112 may be scanned witha known or otherwise determinable vertical displacement.

While scan pattern 300 is illustrated as having vertically displacedscan pattern sections 310, 320 in FIG. 3, in some implementations of theinvention, scan pattern may have horizontally displaced scan sections.In implementations of the invention where lidar subsystem 130 employs ahorizontally displaced scan pattern (not otherwise illustrated), firstbeam 112 is displaced horizontally (i.e., by some horizontal distance,angle of azimuth, or other horizontal displacement) from second beam112. In this way, the pair of beams 112 may be scanned with a known orotherwise determinable horizontal displacement.

While FIG. 3 illustrates a scan pattern 300 with two verticallydisplaced scan pattern sections 310, 320, various numbers of beams maybe stacked to create a corresponding number of scan pattern sections aswould be appreciated. For example, three beams may be configured witheither vertical displacements or horizontal displacements to providethree scan pattern sections. Other numbers of beams may be used eitherhorizontally or vertically as would be appreciated.

FIG. 4 illustrates a scan pattern 400 for lidar subsystem 130 thatemploys four beams 112 according to various implementations of theinvention. As illustrated in FIG. 4, lidar subsystem 130 includes fourbeams 112 arranged to scan a scan pattern 400. Scan pattern 400 may beachieved by having a first pair of beams 112 displaced horizontally fromone another and a second pair of beams 112 displaced horizontally fromone another and vertically from the first pair of beam 112, therebyforming a rectangular scanning arrangement. Other scanning geometriesmay be used as would be apparent. Scan pattern 400 may be achieved bycontrolling the beams independently from one another, as pairs (eitherhorizontally or vertically), or collectively, via beam scanningmechanism(s) 140.

Scan pattern 400 includes a first scan pattern section 410, a secondscan pattern section 420, a third scan pattern section 430, and a fourthscan pattern section 440. In some implementations of the invention, eachof the respective scan pattern sections 410, 420, 430, 440 may overlapan adjacent scan pattern portion by some amount (illustratedcollectively in FIG. 4 as overlap regions 450). For example, in someimplementations of the invention, scan pattern 400 includes an overlapregion 450 between first scan pattern section 410 and third scan patternsection 430. Likewise, an overlap region 450 exists between a first scanpattern section 410 and a second scan section 420. In someimplementations of the invention, various ones of these overlap regions450 may not occur or otherwise be utilized. In some implementations ofthe invention, for example, only vertical overlap regions 450 may occuror be utilized. In some implementations of the invention, onlyhorizontal overlap regions 450 may occur or be utilized. In someimplementations of the invention, no overlap regions 450 may occur or beutilized. In some implementations of the invention, other combinationsof overlap regions 450 may be used.

As illustrated in FIG. 3 and FIG. 4, the use by lidar subsystem 130 ofmultiple beams 112 may increase a rate at which a particular volume (orspecific targets within the volume) may be scanned. For example, a givenvolume may be scanned twice as fast using two beams 112 as opposed toscanning the same volume with one beam 112. Similarly, a given volumemay be scanned twice as fast using four beams 112 as opposed to scanningthe same volume with two beams 112, and four times as fast as scanningthe same volume with one beam 112. In addition, multiple beams 112 maybe used to measure or estimate various parameters associated with themotion of target 190 as will be discussed in more detail below.

According to various implementations of the invention, particular scanpatterns (and their corresponding beam configurations) may be used toprovide measurements and/or estimates of motion aspects of target 190.As described above, each beam 112 may be used to simultaneously providea range measurement and a Doppler velocity measurement at each pointscanned.

In some implementations of the invention, for each beam 112, a pointscanned by that beam 112 may be described by an azimuth angle, anelevation angle, and a time. Each beam 112 provides a range measurementand a Doppler velocity measurement at that point and time. In someimplementations of the invention, each point scanned by beam 112 may beexpressed as an azimuth angle, an elevation angle, a range measurement,a Doppler velocity measurement, and a time. In some implementations ofthe invention, each point scanned by beam 112 may be expressed inCartesian coordinates as a position (x, y, z), a Doppler velocity and atime.

According to various implementations of the invention, measurements fromlidar subsystem 130 (i.e., lidar outputs 116) and measurements fromvideo subsystem 150 (frames 155) may be used to measure and/or estimatevarious orientation and/or motion aspects of target 190. Theseorientation and/or motion aspects of target 190 may include position,velocity, acceleration, angular position, angular velocity, angularacceleration, etc. As these orientation and/or motion aspects aremeasured and/or estimated, a trajectory of target 190 may be determinedor otherwise approximated. In some implementations of the invention,target 190 may be considered a rigid body over a given time interval andits motion may be expressed as translational velocity componentsexpressed in three dimensions as v_(x) ^(trans), v_(y) ^(trans), andv_(z) ^(trans), and angular velocity components expressed in threedimensions as ω_(x), ω_(y), and ω_(z) over the given time interval.Collectively, these translational velocities and angular velocitiescorrespond to six degrees of freedom of motion for target 190 over theparticular time interval. In some implementations of the invention,measurements and/or estimates of these six components may be used toexpress a trajectory for target 190. In some implementations of theinvention, measurements and/or estimates of these six components may beused to merge the three-dimensional image of target 190 obtained fromlidar subsystem 130 with the two-dimensional images of target 190obtained from video subsystem 150 to generate three-dimensional videoimages of target 190.

In some implementations of the invention, the instantaneous velocitycomponent v_(z)(t) of a point on target 190 may be calculated based onthe range measurement, the Doppler velocity measurement, the azimuthangle and the elevation angle from lidar subsystem 130 as would beapparent.

Lidar subsystem 130 may be used to measure and/or estimate translationalvelocity v_(z) ^(trans) and two angular velocities of target 190, namelyω, and ω_(y). For example, FIG. 5 illustrates an exemplary relationshipbetween points with corresponding measurements from two beams 112 thatmay be used to estimate x and y components of angular velocity of target190 according to various implementations of the invention. Moreparticularly, and generally speaking, as illustrated in FIG. 5, inimplementations where beams 112 are displaced from one another along they-axis, a local velocity along the z-axis of point P_(A) determined viaa first beam 112, a velocity of point P_(B) determined via a second beam112, and a distance between P_(A) and P_(B) may be used to estimate anangular velocity of these points about the x-axis (referred to herein asω_(x)) as would be appreciated. In some implementations of theinvention, these measurements may be used to provide an initial estimateof ω_(x).

FIG. 6 illustrates another exemplary relationship between points withcorresponding measurements from two beams 112 that may be used toestimate an angular velocity according to various implementations of theinvention. More particularly, as illustrated in FIG. 6, inimplementations were beams 112 are displaced from one another on target190 along the x-axis, a velocity of point P_(A) determined via a firstbeam 112, a velocity of point P_(B) determined by a second beam 112, anda distance between P_(A) and P_(B) on target 190 along the x-axis may beused to estimate an angular velocity of these points about the y-axis(referred to herein as ω_(y)). In some implementations of the invention,these measurements may be used to provide an initial estimate of ω_(y).

FIG. 5 and FIG. 6 illustrate implementations of the invention where twobeams 112 are disposed from one another along a vertical axis or ahorizontal axis, respectively, and the corresponding range (which may beexpressed in three-dimensional coordinates x, y, and z) and Dopplervelocity at each point are measured at substantially the same time. Inimplementations of the invention that employ beams 112 along a singleaxis (not otherwise illustrated), an angular velocity may be estimatedbased on Doppler velocities measured at different points at differenttimes along the single axis. As would be appreciated, better estimatesof angular velocity may obtained using: 1) measurements at points at theextents of target 190 (i.e., at larger distances from one another), and2) measurements taken within the smallest time interval (so as tominimize any effects due to acceleration).

FIG. 5 and FIG. 6 illustrate conceptual estimation of the angularvelocities about different axes, namely the x-axis and the y-axis. Ingeneral terms, where a first beam 112 is displaced on target 190 along afirst axis from a second beam 112, an angular velocity about a secondaxis orthogonal to the first axis may be determined from the velocitiesalong a third axis orthogonal to both the first and second axes at eachof the respective points.

In some implementations of the invention, where two beams are displacedalong the y-axis from one another (i.e., displaced vertically) andscanned horizontally with vertical separation between scans, estimatesof both ω_(x) and ω_(y) may be made. While simultaneous measurementsalong the x-axis are not available, they should be sufficiently close intime in various implementations to neglect acceleration effects. In someimplementations of the invention where two beams 112 are displaced alongthe x-axis from one another and at least a third beam 112 is displacedalong the y-axis from the pair of beams 112, estimates of ω_(x), ω_(y)and v_(z) ^(trans) may be made. In some implementations of theinvention, estimates of both ω_(x), ω_(y) and v_(z) ^(trans) may be madeusing four beams 112 arranged in a rectangular fashion. In suchimplementations, the measurements obtained from the four beams 112include more information than necessary to estimate ω_(x), ω_(y) andv_(z) ^(trans). This so-called “overdetermined system” may be used toimprove the estimates of ω_(x), ω_(y) and v_(z) ^(trans) as would beappreciated.

As has been described, range and Doppler velocity measurements taken atvarious azimuth and elevation angles and at various points in time bylidar subsystem 130 may be used to estimate translational velocity v_(z)^(trans) and estimate two angular velocities, namely, ω_(x) and ω_(y),for the rigid body undergoing ballistic motion.

In some implementations of the invention, ω_(x), ω_(y) and v_(z)^(trans) may be determined at each measurement time from themeasurements obtained at various points as would be appreciated. In someimplementations of the invention, ω_(x), ω_(y) and v_(z) ^(trans) may beassumed to be constant over an particular interval of time. In someimplementations of the invention, ω_(x), ω_(y) and v_(z) ^(trans) may bedetermined at various measurement times and subsequently averaged over aparticular interval of time to provide estimates of ω_(x), ω_(y) andv_(z) ^(trans) for that particular interval of time as would beappreciated. In some implementations of the invention, the particulartime interval may be fixed or variable depending, for example, on themotion aspects of target 190. In some implementations of the invention,a least squares estimator may be used to provide estimates of ω_(x),ω_(y) and v_(z) ^(trans) over a particular interval of time as would beappreciated. Estimates of ω_(x), ω_(y) and v_(z) ^(trans) may beobtained in other manners as would be appreciated.

In some implementations of the invention, images from video subsystem150 may be used to estimate three other motion aspects of target 190,namely translational velocity components v_(x) ^(trans) and v_(y)^(trans) and angular velocity component ω_(z) over a given interval oftime. In some implementations of the invention, frames 155 captured byvideo subsystem 150 may be used to estimate x and y components ofvelocity for points on target 190 as it moves between frames 155. FIG. 7illustrates a change in position of a particular point or feature I_(A)between a frame 155 at time T and a frame 155 at subsequent time T+Δt.

In some implementations of the invention, this change of position isdetermined for each of at least two particular points or features inframe 155 (not otherwise illustrated). In some implementations of theinvention, the change of position is determined for each of many pointsor features. In some implementations of the invention, translationalvelocity components v_(x) ^(trans) and v_(y) ^(trans), and angularvelocity component ω_(z) of target 190 may be estimated based on adifference in position of a feature I_(A)(T) and I_(A)(T+Δt) and adifference in time, Δt, between the frames 155. These differences inposition and time may be used to determine certain velocities of thefeature, namely, v_(x) ^(feat) and v_(y) ^(feat) that may in turn beused to estimate the translational velocity components v_(x) ^(trans)and v_(y) ^(trans), and angular velocity component ω_(z) of target 190.Such estimations of velocity and angular velocity of features betweenimage frames are generally understood as would be appreciated.

In some implementations of the invention, many features of target 190are extracted from consecutive frames 155. The velocities v_(x) ^(feat)and v_(y) ^(feat) of these features over the time interval betweenconsecutive frames 155 may be determined based on changes in position ofeach respective feature between the consecutive frames 155. A leastsquares estimator may be used to estimate the translational velocitiesv_(x) ^(trans) and v_(y) ^(trans), and the angular velocity ω_(z) fromthe position changes of each the extracted features.

In some implementations of the invention, a least squares estimator mayuse measurements from lidar subsystem 130 and the changes in position ofthe features in frames 155 from video subsystem 150 to estimate thetranslational velocities v_(x) ^(trans), v_(y) ^(trans) and v_(z)^(trans) and the angular velocities ω_(x), ω_(y), and ω_(z) of target190.

As has been described above, lidar subsystem 130 and video subsystem 150may be used to estimate six components that may be used describe themotion of target 190. These components of motion may be collected overtime to calculate a trajectory of target 190. This trajectory may thenbe used to compensate for motion of target 190 to obtain a motionstabilized three dimensional image of target 190. In variousimplementations of the invention, the trajectory of target 190 may beassumed to represent ballistic motion over various intervals of time.The more accurately trajectories of target 190 may be determined, themore accurately combined system 100 may adjust the measurements oftarget 190 to, for example, represent three dimensional images, or otheraspects, of target 190.

In various implementations of the invention, a rate at whichmeasurements are taken by lidar subsystem 130 is different from a rateat which frames 155 are captured by video subsystem 150. In someimplementations of the invention, a rate at which measurements are takenby lidar subsystem 130 is substantially higher than a rate at whichframes 155 are captured by video subsystem 150. In addition, becausebeams 112 are scanned through a scan volume by lidar subsystem 130,measurements at different points in the scan volume may be taken atdifferent times from one another; whereas pixels in a given frame 155are captured substantially simultaneously (within the context of videoimaging). In some implementations of the invention, these timedifferences are resolved in order to provide a more accurate trajectoryof target 190.

As illustrated in FIG. 8, in some implementations of the invention, ascan pattern 840 may be used to scan a volume for targets. For purposesof explanation, scan pattern 840 represents a pattern of measurementstaken by a single beam. In some implementations multiple beams may beused, each with their corresponding scan pattern as would be apparent.As illustrated, scan pattern 840 includes individual points 810 measuredleft to right in azimuth at a first elevation 831, right to left inazimuth at a second elevation 832, left to right in azimuth at a thirdelevation 833, etc., until a particular scan volume is scanned. In someimplementations, scan pattern 840 may be divided into intervalscorresponding to various timing aspects associated with combined system100. For example, in some implementations of the invention, scan pattern840 may be divided into time intervals associated with a frame rate ofvideo subsystem 150. In some implementations of the invention, scanpattern 840 may be divided into time intervals associated with scanninga particular elevation (i.e., an entire left-to-right or right-to-leftscan). In some implementations of the invention, scan pattern 840 may bedivided into time intervals associated with a roundtrip scan 820(illustrated in FIG. 8 as a roundtrip scan 820A, a roundtrip scan 820B,and a roundtrip scan 820C) at one or more elevations (i.e., aleft-to-right and a return right-to-left scan at either the same ordifferent elevations). Similar timing aspects may be used inimplementations that scan vertically in elevation (as opposed tohorizontally in azimuth). Other timing aspects may be used as well.

As illustrated in FIG. 8 and again for purposes of explanation, eachinterval may include N points 810 which may in turn correspond to thenumber of points 810 in a single scan (e.g., 831, 832, 833, etc.) or ina roundtrip scan 820. A collection of points 810 for a particularinterval is referred to herein as a sub-point cloud and a collection ofpoints 810 for a complete scan pattern 840 is referred to herein as apoint cloud. In some implementations of the invention, each point 810corresponds to the lidar measurements of range and Doppler velocity at aparticular azimuth, elevation, and a time at which the measurement wastaken. In some implementations of the invention, each point 810corresponds to the lidar measurements of range (expressed x, y, zcoordinates) and Doppler velocity and a time at which the measurementwas taken.

FIG. 9 illustrates a timing diagram 900 useful for describing varioustiming aspects associated with measurements from lidar subsystem 130according to various implementations of the invention. Timing diagram900 includes points 810 scanned by beam 112, sub-point clouds 920 formedfrom a plurality of points 810 collected over an interval correspondingto a respective sub-point cloud 920, and a point cloud 930 formed from aplurality of sub-point clouds 920 collected over the scan pattern.Timing diagram 900 may be extended to encompass points 810 scanned bymultiple beams 112 as would be appreciated.

Each point 810 is scanned by a beam 112 and measurements associated witheach point 810 are determined by lidar subsystem 130. In someimplementations of the invention, points 810 are scanned via a scanpattern (or scan pattern section). The interval during which lidarsubsystem 130 collects measurements for a particular sub-point cloud 920may have a time duration referred to as T_(SPC). In some implementationsof the invention, the differences in timing of the measurementsassociated with individual points 810 in sub-point cloud 920 may beaccommodated by using the motion aspects (e.g., translational velocitiesand angular velocities) for each point to adjust that point to aparticular reference time for sub-point cloud 920 (e.g., t_(RSPC)). Thisprocess may be referred to as stabilizing the individual points 810 forthe motion aspects of target 190.

In some implementations of the invention, the velocities may be assumedto be constant over the time interval (i.e., during the time durationT_(SPC)). In some implementations of the invention, the velocities maynot be assumed to be constant during the period of the scan pattern andacceleration effects may need to be considered to adjust themeasurements of points 810 to the reference time as would beappreciated. In some implementations of the invention, adjustments dueto subdivision of the time interval may also need to be accommodated. Asillustrated in FIG. 9, the reference time for each sub-point cloud 920may be selected at the midpoint of the interval, although otherreference times may be used.

In some implementations of the invention, similar adjustments may bemade when combining sub-point clouds 920 into point clouds 930. Moreparticularly, in some implementations of the invention, the differencesin timing of the measurements associated with sub-point clouds 920 inpoint cloud 930 may be accommodated by using the motion aspectsassociated with the measurements.

In some implementations of the invention, the measurements associatedwith each sub-point cloud 920 that is merged into point cloud 930 areindividually adjusted to a reference time associated with point cloud930. In some implementations of the invention, the reference timecorresponds to a frame time (e.g., time associated with a frame 155). Inother implementations of the invention, the reference time correspond toan earliest of the measurement times of points 1110 in point cloud 930,a latest of the measurement times of points 1110 in point cloud 930, anaverage or midpoint of the measurement times of points 1110 in pointcloud 930, or other reference time associated with point cloud 930.

Although not otherwise illustrated, in some implementations of theinvention, similar adjustments may be made to combine point clouds 930from individual beams 112 into aggregate point clouds at a particularreference time. In some implementations of the invention, this may beaccomplished at the individual point level, the sub-point cloud level orthe point cloud level as would be appreciated. For purposes of theremainder of this description, sub-point clouds 920 and point clouds 930refer to the collection of points 810 at their respective referencetimes from each of beams 112 employed by lidar subsystem 130 to scantarget 190.

In some implementations of the invention, motion aspects of target 190may be assumed to be constant over various time intervals. For example,motion aspects of target 190 may be assumed to be constant over T_(SPC)or other time duration. In some implementations of the invention, motionaspects of target 190 may be assumed to be constant over a givenT_(SPC), but not necessarily constant over T_(PC). In someimplementations of the invention, motion aspects of target 190 may beassumed to be constant over incremental portions of T_(SPC), but notnecessarily over the entire T_(SPC). As a result, in someimplementations of the invention, a trajectory of target 190 may beexpressed as a piece-wise function of time, with each “piece”corresponding to the motion aspects of target 190 over each individualtime interval.

In some implementations, timing adjustments to compensate for motion maybe expressed as a transformation that accounts for the motion of a pointfrom a first time to a second time. This transformation, when applied tomeasurements from, for example, lidar subsystem 130, may perform thetiming adjustment from the measurement time associated with a particularpoint (or sub-point cloud or point cloud, etc.) to the desired referencetime. Furthermore, when the measurements are expressed as vectors, thistransformation may be expressed as a transformation matrix. Suchtransformation matrices and their properties are generally well known.

As would be appreciated, the transformation matrices may be readily usedto place a position and orientation vector for a point at any time to acorresponding position and orientation vector for that point at anyother time, either forwards or backwards in time, based on the motion oftarget 190. The transformation matrices may be applied to sub-pointclouds, multiple sub-point clouds and point clouds as well. In someimplementations, a transformation matrix may be determined for eachinterval (or subinterval) such that it may be used to adjust a pointcloud expressed in one interval to a point cloud expressed in the nextsequential interval. In these implementations, each interval has atransformation matrix associated therewith for adjusting the pointclouds for the trajectory of target 190 to the next interval. In someimplementations, a transformation matrix may be determined for eachinterval (or subinterval) such that it may be used to adjust a pointcloud expressed in one interval to a point cloud expressed in the priorsequential interval. Using the transformation matrices for variousintervals, a point cloud can be referenced to any time, either forwardor backward.

FIG. 10 illustrates a timing diagram 1000 useful for describing varioustiming aspects associated with measurements from lidar subsystem 130 inrelation to measurements from video subsystem 150 according to variousimplementations of the invention. In some implementations of theinvention, point cloud 930 may be referenced to the midpoint of a timeinterval between frames 155 or other time between frames 155. In someimplementations of the invention, point cloud 930 may be referenced to aframe time corresponding to a particular frame 155. Point cloud 930 maybe referenced in other manners relative to a particular frame 155 aswould be appreciated.

As illustrated in FIG. 10, PC_(m−1) is the expression of point cloud 930referenced at the frame time of frame I_(n−1); PC_(m) is the expressionof point cloud 930 referenced at the frame time of frame I_(n); andPC_(m+1) is the expression of point cloud 930 referenced at the frametime of frame I_(n+1); and PC_(m+2) is the expression of point cloud 930referenced at the frame time of frame I_(n+2). In some implementations,point cloud 930 may be referenced at other times in relation to theframes and frames times as would be apparent.

As described above, a transformation matrix T_(i,i+1) may be determinedto transform an expression of point cloud 930 at the i^(th) frame timeto an expression of point cloud 930 at the (i+1)^(th) frame time. Inreference to FIG. 10, a transformation matrix T_(m−1,m) may be used totransform PC_(m−1) to PC_(m); a transformation matrix T_(m,m+1) may beused to transform PC_(m) to PC_(m+1); and a transformation matrixT_(m+1,m+2) may be used to transform PC_(m+1) to PC_(m+2). In this way,transformation matrices may be used to express point clouds 930 atdifferent times corresponding to frames 155.

According to various implementations of the invention, thetransformation matrices which are applied to point cloud 930 to expresspoint cloud 930 from a first time to a second time are determined indifferent processing stages. Generally speaking, transformation matricesare directly related with six degree of motion parameters ω_(x), ω_(y),ω_(z), v_(x) ^(trans), v_(y) ^(trans) and v_(z) ^(trans) that may becalculated in two steps: first ω_(x), ω_(y), and v_(z) ^(trans) fromlidar subsystem and second v_(x) ^(trans), v_(y) ^(trans) and ω_(z),from video subsystem.

FIG. 11 illustrates a block diagram of a configuration of processingsystem 160 that may be used during a first phase of the first processingstage to estimate a trajectory of target 190 according to variousimplementations of the invention. In some implementations of theinvention, during the first phase of the first stage, a series ofinitial transformation matrices (referred to herein as T_(i,i+1) ⁽⁰⁾)are determined from various estimates of the motion aspects of target190. As illustrated, lidar subsystem 130 provides range, Dopplervelocity, azimuth, elevation and time for at each point as input to aleast squares estimator 1110 that is configured to estimate angularvelocities ω_(x) and ω_(y) and translational velocity v_(z) ^(trans)over each of a series of time intervals. In some implementations of theinvention, angular velocities ω_(x) and ω_(y) and translational velocityv_(z) ^(trans) are iteratively estimated by varying the size of the timeintervals (or breaking the time intervals into subintervals) asdiscussed above until any residual errors from least squares estimator1110 for each particular time interval reach acceptable levels as wouldbe apparent. This process may be repeated for each successive timeinterval during the time measurements of target 190 are taken by lidarsubsystem 130.

Assuming that target 190 can be represented over a given time intervalas a rigid body (i.e., points on the surface of target 190 remain fixedwith respect to one another) undergoing ballistic motion (i.e., constantvelocity with no acceleration), an instantaneous velocity of any givenpoint 810 on target 190 can be expressed as:

v=v ^(trans)+[ω×(R−R _(c) −v ^(trans) *Δt)]  Eq. (1)

where

-   -   v is the instantaneous velocity vector of the given point;    -   v^(trans) is the translational velocity vector of the rigid        body;    -   ω the rotational velocity vector of the rigid body;    -   R is the position of the given point on the target;    -   R_(c) is the center of rotation for the target; and    -   Δt is the time difference of each measurement time from a given        reference time.

Given the measurements available from lidar subsystem 130, thez-component of the instantaneous velocity may be expressed as:

v _(z) =v _(z) ^(trans)+[ω×(R−R _(c) −v ^(trans) *Δt)]_(z)  Eq. (2)

where

-   -   v_(z) is the z-component of the instantaneous velocity vector;    -   v_(z) ^(trans) is the z-component of the translational velocity        vector; and    -   [ω×(R−R_(c)−v^(trans)*Δt)]_(z) is the z-component of the cross        product.

In some implementations of the invention, frame-to-frame measurementscorresponding to various features from images 155 may be made. Thesemeasurements may correspond to a position (e.g., x^(feat), y^(feat)) anda velocity (e.g., v_(x) ^(feat), v_(y) ^(feat)) for each of the featuresand for each frame-to-frame time interval. In implementations where az-coordinate of position is not available from video subsystem 150, aninitial estimate of z may be made using, for example, an average zcomponent from the points from lidar subsystem 130. Least squaresestimator 1120 estimates angular velocities ω_(x), ω_(y), and ω_(z) andtranslational velocities v_(x) ^(trans), v_(y) ^(trans), and v_(z)^(trans) which may be expressed as a transformation matrix T_(i,i+1) ⁽⁰⁾for each of the relevant time intervals. In some implementations of theinvention, a cumulative transformation matrix corresponding to thearbitrary frame to frame time interval may be determined.

FIG. 12 illustrates a block diagram of a configuration of processingsystem 160 that may be used during a second phase of the firstprocessing stage to estimate a trajectory of target 190 according tovarious implementations of the invention. In some implementations of theinvention, during the second phase of the first stage, newtransformation matrices (referred to herein as T_(i,i+1) ⁽¹⁾) aredetermined from various estimates of the motion aspects of target 190.As illustrated, measurements from lidar subsystem 130 of range, Dopplervelocity, azimuth, elevation and time for at each of the N points areinput to a least squares estimator 1110 of processing system 160 alongwith the transformation matrices T_(i,i+1) ⁽⁰⁾ to estimate angularvelocities ω_(x) and ω_(y) and translational velocity v_(z) ^(trans)over each of a series of time intervals in a manner similar to thatdescribed above during the first phase.

The primary difference between the second phase and the first phase isthat least squares estimator 1120 uses the calculated z position of thefeatures based on T_(i,i+1) ⁽⁰⁾ as opposed to merely an average of zposition. Least squares estimator 1120 estimates new angular velocitiesω_(x), ω_(y), and ω_(z) and new translational velocities v_(x) ^(trans),v_(y) ^(trans), and v_(z) ^(trans) which may be expressed as atransformation matrix T_(i,i+1) ⁽¹⁾ for each of the relevant timeintervals. Again, in some implementations of the invention, a cumulativetransformation matrix corresponding to the frame to frame time intervalmay be determined.

FIG. 13 illustrates a block diagram of a configuration of processingsystem 160 that may be used during a third phase of the first processingstage to estimate a trajectory of target 190 according to variousimplementations of the invention. In some implementations of theinvention, during the third phase of the first stage, new transformationmatrices (referred to herein as T_(i,i+1) ⁽²⁾) are determined fromvarious estimates of the motion aspects of target 190. As illustrated,lidar subsystem 130 provides range, Doppler velocity, azimuth, elevationand time for at each of the points as input to a least squares estimator1110 to estimate angular velocities ω_(x) and ω_(y) and translationalvelocity v_(z) ^(trans) over each of a series of time intervals in amanner similar to that described above during the first phase. In thisphase, calculated values of v_(x) and v_(y) for each point based onT_(i,i+1) ⁽¹⁾ as determined during the prior phase are input into leastsquares estimator 1120 as opposed to the feature measurements usedabove.

The primary difference between the third phase and the second phase isthat least squares estimator 1120 uses T_(i,i+1) ⁽¹⁾ to describe motionbetween the relevant frames 155. Least squares estimators 1110, 1120estimate new angular velocities ω_(x), ω_(y), and ω_(z) and newtranslational velocities v_(x) ^(trans), v_(y) ^(trans), and v_(z)^(trans) which may be expressed as a transformation matrix T_(i,i+1) ⁽²⁾for each of the relevant time intervals. Again, in some implementationsof the invention, a cumulative transformation matrix corresponding tothe frame to frame time interval may be determined.

In various implementations of the invention, any of the phases of thefirst processing stage may be iterated any number of times as additionalinformation is gained regarding motion of target 190. For example, asthe transformation matrices are improved, each point 810 may be betterexpressed at a given reference time in relation to its measurement time.

During the first processing stage, the translational velocities of eachpoint (not otherwise available from the lidar measurements) may beestimated using features from the frames 155. Once all velocitycomponents are known or estimated for each point, transformationmatrices may be determined without using the feature measurements asillustrated in FIG. 13.

FIG. 14 illustrates a block diagram of a configuration of processingsystem 160 that may be used during a first phase of the secondprocessing stage to refine a trajectory of target 190 according tovarious implementations of the invention. The first processing stageprovides transformation matrices sufficient to enable images 155 to bemapped onto images at any of the frame times. Once so mapped,differences in pixels themselves (as opposed to features in images 155)from different images transformed to the same frame time may be used tofurther refine the trajectory of target 190. In some implementations,various multi-frame corrections may be determined, which in turn throughthe least square estimator can be used for obtaining offsets between theconsecutive images Δx_(i,i+1), Δy_(i,i+1), Δθz_(i,i+1). Thesecorrections may be used to refine the transformation matrices (forexample, matrices T_(i,i+1) ⁽²⁾ to T_(i,i+1) ⁽³⁾). In someimplementations of the invention, during the first phase of the secondprocessing stage, a series of new transformation matrices (referred toherein as T_(i,i+1) ⁽³⁾) are refinements of T_(i,i+1) ⁽²⁾ on the basisof the offsets between image I_(i) and an image I_(j), namely, Δx_(i,j),Δy_(i,j), Δθz_(i,j). As illustrated, an estimator 1410 determines adifference between an image I_(i) and an image using the appropriatetransformation matrix T_(i,j) ⁽²⁾ to express the images at the sameframe time.

FIG. 15 illustrates a block diagram of a configuration of processingsystem 160 that may be used during a second phase of the secondprocessing stage to further refine a trajectory of target 190 accordingto various implementations of the invention. To the extent thatadditional accuracy is necessary, the transformation matrices from thefirst phase of the second processing stage (e.g., T_(i,i+1) ⁽³⁾) may beused in connection with the measurements from lidar subsystem 130 tofurther refine the transformation matrices (referred to herein asT_(i,i+1) ⁽⁴⁾). In some implementations of the invention, during thisphase, measurements from lidar subsystem 130 that occur within anyoverlap regions 360, 450 are used. These measurements correspond tomultiple measurements taken for the same point (or substantially thesame point) at different times. This phase is based on the premise thatcoordinate measurements of the same point on target 190 taken differenttimes should transform precisely to one another with a perfecttransformation matrix, i. e. points measured at the different times thathave the same x and y coordinates should have the same z coordinate. Inother words, all coordinates of the underlying points should directlymap to one another at the different points in time. The differences in zcoordinates (i.e., corrections) between the measurements at differenttimes can be extracted and input to the least square estimator. Throughthe least square estimator, the corrections to the transformationparameters between the consecutive frames may obtained and may beexpressed as Δz_(i,i+1), Δθx_(i,i+1), and Δθy_(i,i+1). These correctionsmay be used to refine the transformation matrices T_(i,i+1) ⁽³⁾ toT_(i,i+1) ⁽⁴⁾. In some implementations of the invention, multiplemeasurements corresponding to use of an overscan beam may be used in asimilar manner.

Various implementations of invention calibrate lidar subsystem 130 withvideo subsystem 150. In some implementations, calibrating the lidarsubsystem 130 with the video subsystem 150 includes two stages. In someimplementations, in a first stage, processing system 160 may calibratethe lidar subsystem so that lidar measurements provide 3D lidarcoordinates. In some implementations, a 3D lidar coordinate correspondsto the lidar measurements of range and Doppler velocity at a particularazimuth, elevation, and a time at which the measurement was taken. Insome implementations, in a second stage, processing system 160 mayrelate the 3D lidar coordinates with a video image obtained from thevideo subsystem 150.

In some implementations, processing system 160 may utilize a referencegrid 1600 (illustrated in FIG. 16, for example) to calibrate the lidarsubsystem 130, the video subsystem 150, and the lidar subsystem 130 withthe video subsystem 150. In some implementations, reference grid 1600may be considered as target 190 for calibration purposes. In someimplementations, the reference grid 1600 may be manufactured withaccuracy specifications that surpass the accuracy of the lidar subsystem130 by at least an order of the magnitude.

In some implementations, reference grid 1600 may include a plurality ofhighly reflective rectangular tapes 1610 ₁, 1610 ₂, . . . , 1610 _(n),along each edge of the reference grid 1600 (illustrated along edge 1 ofreference grid 1600 in FIG. 16, for example). In other words, each edge(edge 1, edge 2, edge 3, and edge 4) of the reference grid 1600 mayinclude a plurality of highly reflective rectangular tapes 1610 ₁, 1610₂, . . . , 1610 _(n). In some implementations, reference grid 1600 mayalso include a plurality of black round video targets 1620 ₁, 1620 ₂, .. . , 1620 _(n) interspersed throughout a surface of the reference grid1600.

In some implementations, calibrating the lidar subsystem 130 may includematching the actual locations of each of the highly reflective tapes1610 ₁, 1610 ₂, . . . , 1610 _(n) along each edge of the reference grid1600 to the lidar measurements from the lidar subsystem 130. In someimplementations, in the lidar subsystem 130, a first beam may beselected as the “master beam” and the coordinate system may be definedrelative to the measurements of the “master beam” (i.e., lidarmeasurements for each of a plurality of points on the reference grid forthe “master” beam). In some implementations, the edges of the highlyreflective tapes may be determined/extracted by scanning the referencegrid 1600 with multiple beams and by finding the appropriate thresholdfor the lidar SNR (Signal to Noise Ratio). In some implementations, thereadings of the beam steering and lidar range measurements may berelated to the values of the XYZ coordinates by finding the appropriatepolynomial coefficients in the framework of the least squareoptimization using the nominal positions of the highly reflective tapes.In some implementations, for lidar subsystems employing multiple beamsand multiple beam steering systems, the same procedure may be repeatedfor each system and various transformation parameters may be determinedfor transforming the lidar measurements from each of the non “master”beams in their respective coordinate frames to that of the coordinateframe of the “master” beam, as would be appreciated.

In some implementations, calibrating the lidar subsystem 130 may includegenerating the lidar measurements for each of the plurality of points onthe reference grid 1600 at various ranges. For example, the referencegrid 1600 may be placed at different ranges (e.g., distances) from thelidar subsystem 130, and the lidar subsystem 130 may generate lidarmeasurements at each range. In some implementations, processing system160 may determine lidar measurements for the locations of each of thehighly reflective tap spots 1610 ₁, 1610 ₂, . . . , 1610 _(n) along eachedge of the reference grid 1600 at each range.

In some implementations, calibrating the lidar subsystem with the videosubsystem includes relating the 3D lidar measurements (XYZ) to therespective pixels on the video image. In some implementations, tocalibrate the video subsystem 150, processing system 160 may utilize aprocess referred to as “range cell video calibration.” In someimplementations, video subsystem 150 may capture two dimensional imagesof the reference grid 1600 at various ranges (the same ranges as usedfor the lidar subsystem 130). In some implementations, having the lidarmeasurements for each of the highly reflective tapes 1610 ₁, 1610 ₂, . .. , 1610 _(n) along each edge of the reference grid 1600 at variousranges allows obtaining the respective coordinates of the video targets1620 _(i), 1620 ₂, . . . , 1620 _(n) (since the positions of the videotargets are known relative to the highly reflective tapes). In someimplementations, processing system 160 may, at each range, compare the3D coordinates of the video targets 1620 ₁, 1620 ₂, . . . , 1620 _(n)against the pixel coordinates of the video targets 1620 ₁, 1620 ₂, . . ., 1620 _(n) from the video subsystem 150. In some implementations,having all video targets 1620 ₁, 1620 ₂, . . . , 1620 _(n) on the plane,projective transformations may be determined to relate the pixelcoordinates of the video targets to the 3D coordinates of the videotargets as would be appreciated. Thus, the XYZ coordinate on the planerelates to the respective pixel values and vice versa, the pixel valueon the plane relates to the XYZ coordinate.

In some implementations, the generic relation between XYZ coordinate andpixel values (for example XYZ coordinate to pixel values and vice versa)requires a minimum of two range cells, such that having an arbitrary XYZcoordinate, the respective pixel values may be interpolated/extrapolatedbetween the different cells. Similarly, having pixel values and relativeposition between the range cells allows obtaining the XYZ coordinates.In some implementations, the video subsystem 150 may be calibrated usingrange cells with imaginary z=const plane, i. e. the arbitrary positionof the reference grid is projected to the z=const cell where the valueof the z may be chosen to be close to the average z position of thereference grid. Having defined the z=const range cells, both XYZcoordinates and video pixels may be projected to the z=const plane.Particularly, the XYZ coordinates on the plane may be determined fromthe intersection of the radial beam with the z=const plane, while thepixel projections are more subtle. Firstly, from the projectivetransformations obtained from two different reference grid measurementsthe line connecting the same pixels going from one range cell to anotheris found (this line may not cross the center of the coordinate system,because the camera may not be aligned with the “master” beam). Secondly,the intersection of this line with z=const plane is obtained, whichwould deviate from the lidar projection point. Lastly, from thedeviation of the XYZ intersections of the z=const plane, the pixelsvalues are found iteratively. Once the lidar XYZ measurements and pixelvalues are projected to the z=const plane, the respective projectivetransformations may be found for each z=const plane. Thus, the videocalibration may be reduced to the plane (z=const) measurements atdifferent ranges, wherein the 3D coordinates correspond to the pixelpositions on the z=const plane.

In some implementations, multiple reference grid measurements (forexample at different azimuth and/or elevation positions) made within thesame z range tolerance can can be projected to the z=const plane in thesimilar manner, and the respective projective transformations can beobtained.

In some implementations, for the measurements between the range cells,lidar measurements (e.g., lidar 3D coordinates) may be generated and therespective pixel position may be interpolated/extrapolated between therespective range cells, which also accounts for the varying video focusvalue between the respective range cells.

In some implementations, as a result of such calibration, variousmeasurements may be transformed into other reference/measurements aswould be appreciated. For example, for each lidar measured point (3Dcoordinate), the respective pixel positions may be determined. Inaddition, from pixel positions and lidar range measurements the 3Dcoordinates can be found. Other transformations may be determined aswould be appreciated.

In some implementations, FIG. 17 illustrates a flowchart 1700 depictingexample operations performed by system 100 for calibrating the lidarsubsystem 130 and video subsystem 150, according to various aspects ofthe invention. In some implementations, the described operations may beaccomplished using one or more of the components described herein. Insome implementations, various operations may be performed in differentsequences. In other implementations, additional operations may beperformed along with some or all of the operations shown in FIG. 17. Inyet other implementations, one or more operations may be performedsimultaneously. In yet other implementations, one or more operations maynot be performed. Accordingly, the operations described in FIG. 17 andother drawing figures are exemplary in nature and, as such, should notbe viewed as limiting.

In some implementations, in a operation 1702, process 1700 may receivelidar measurements for each of a plurality of points on a reference gridtarget 1600 at various ranges. In some implementations, in an operation1704, process 1700 may receive a plurality of two-dimensional images ofthe reference grid target 1600 at the various ranges.

In some implementations, in an operation 1706, process 1700 maydetermine a lidar measurement for each of the plurality of highlyreflective tapes along each edge of the reference grid target from amongthe received lidar measurements for each of the plurality of points. Insome implementations, in an operation 1708, process 1700 may determine3D coordinates of each of the plurality of video targets on thereference grid target based at least on the lidar measurement for eachof the plurality of highly reflective tapes along each edge of thereference grid target. In some implementations, process 1700 maydetermine the 3D coordinates of each of the plurality of video targetsbased on the lidar measurement for each of the plurality of highlyreflective tapes and the known coordinates (position) of the each of theplurality of video targets relative to the plurality of highlyreflective tapes.

In some implementations, in an operation 1710, process 1700 may relatethe 3D coordinates of each of the plurality of video targets with pixelcoordinates of each of the plurality of video targets, wherein the pixelcoordinates are obtained from an image of the reference grid target.

While the invention has been described herein in terms of variousimplementations, it is not so limited and is limited only by the scopeof the following claims, as would be apparent to one skilled in the art.These and other implementations of the invention will become apparentupon consideration of the disclosure provided above and the accompanyingfigures. In addition, various components and features described withrespect to one implementation of the invention may be used in otherimplementations as well.

What is claimed is:
 1. A system for calibrating a lidar subsystem and avideo subsystem, the system comprising: a lidar subsystem configured todirect a first beam toward a reference grid target and generate a lidarmeasurement for each of a plurality of points on the reference gridtarget for the first beam, wherein the reference grid target comprises aplurality of highly reflective tapes along each edge of the referencegrid target and a plurality of video targets interspersed throughout asurface of the reference grid target; a video subsystem configured toprovide a plurality of two-dimensional images of the reference gridtarget; and a processor configured to: receive, from the lidarsubsystem, the lidar measurement for each of the plurality of points onthe reference grid target, receive, from the video subsystem, theplurality of images of the reference grid target, determine a lidarmeasurement for each of the plurality of highly reflective tapes alongeach edge of the reference grid target from among the received lidarmeasurement for each of the plurality of points on the reference gridtarget; determine 3D coordinates of each of the plurality of videotargets based at least on the lidar measurement for each of theplurality of highly reflective tapes along each edge of the referencegrid target; and relate the 3D coordinates of each of the plurality ofvideo targets with pixel coordinates of each of the plurality of videotargets, wherein the pixel coordinates are obtained from an image of thereference grid target.
 2. The system of claim 1, wherein the lidarmeasurement for each of the plurality of points comprises 3D lidarcoordinates corresponding to the lidar measurement of range and Dopplervelocity at a particular azimuth, elevation, and a time at which themeasurement was taken.
 3. The system of claim 1, wherein the lidarsubsystem is configured to generate a first lidar measurement for eachof the plurality of points on the reference grid target at a firstrange, wherein the video subsystem is configured to provide a firstimage of the reference grid target at the first range, and wherein theprocessor is further configured to: determine a first lidar measurementfor each of the plurality of highly reflective tapes along each edge ofthe reference grid target at the first range; determine, at the firstrange, first 3D coordinates of each of the plurality of video targetsbased at least on the first lidar measurement for each of the pluralityof highly reflective tapes; and relates the first 3D coordinates of eachof the plurality of video targets with pixel coordinates of theplurality of video targets, wherein the pixel coordinates are obtainedfrom the first image.
 4. The system of claim 3, wherein the lidarsubsystem is configured to generate a second lidar measurement for eachof the plurality of points on the reference grid target at a secondrange, wherein the video subsystem is configured to provide a secondimage of the reference grid target at the second range, and wherein theprocessor is further configured to: determine a second lidar measurementfor each of the plurality of highly reflective tapes along each edge ofthe reference grid target at the second range; determines, at the secondrange, second 3D coordinates of each of the plurality of video targetsbased at least on the second lidar measurement for each of the pluralityof highly reflective tapes; and relates the second 3D coordinates ofeach of the plurality of video targets with pixel coordinates of theplurality of video targets, wherein the pixel coordinates are obtainedfrom the second image.